Peter Lynch, the fantastic manager of the Fidelity Magellan fund and the author of One Up on Wall Street, said that a good stock picker will be right six times out of 10. Using some advanced math, I have derived a corollary showing that a good stock picker will also be wrong four times out of 10.

This has nothing to do with throwing darts at The Wall Street Journal, nor are we likely to find monkeys that will hit that six-for-10 mark. These statistics apply to seasoned stock pickers who are getting down and dirty in the research process, trying to pick the very best stocks out there.

Though these top-notch investors may be wrong at times, they are extremely disciplined, and they keep themselves from committing costly unforced errors. If only I could say the same.

I swung at a wild pitch
Roughly two years ago now, I decided to purchase some shares of Scottish Re Group, a reinsurer similar to Berkshire Hathaway's General Re and XL Capital (NYSE:XL). But Scottish Re's management had been too aggressive with its tax planning, and its ill-conceived strategy came back around to bite it, in the form of big write-offs on its deferred tax assets. With the losses came downgrades from ratings agencies, a loss of confidence from some customers, an almost complete turnover of management, and a massive sell-off in the stock.

That's where I stepped in front of the oncoming freight train. I thought the stock price at the time undervalued the assets that the company still had on its books. I even had some confirmation bias in the form of a big investment in the company from Cerberus Capital and MassMutual.

Unfortunately, Scottish Re's core business was never particularly good. The same management team that had botched the company's tax planning also tried to jack up the company's investment portfolio returns by investing in structured mortgage debt -- including very (un)healthy amounts of subprime mortgage debt. You can probably guess where the story went from there.

The agony of unforced errors
There's a simple reason why mortal investors never go 10 out of 10: It's impossible to predict the future. Companies that seem solid, even high- quality, can turn out to be the exact opposite, splattering your portfolio with red ink.

Take Bank of America, for example. Sure, there are plenty of people who would now say "you should have seen the signs," but five years ago, many -- including me -- thought B of A to be a high-quality leader in the banking sector. Unfortunately, it turns out that the company was taking on too much lending risk at the wrong time and had an unhealthy appetite for money-losing organizations (see: Countrywide and Merrill Lynch).

But I'll take a swing and a miss on Bank of America. I was wrong, but I was wrong after having concluded that it was an admirable business with solid leadership. With Scottish Re, I knew it was a mediocre business and that it had just kicked out some very questionable managers, but I chased it anyway. That's a blooper that'll make me cringe for a long time.

3,943 stocks
With more than 3,000 publicly traded companies worth $100 million or more, there's no reason why any investor should have to settle for a mediocre business. (To say nothing of a high valuation, a management team that doesn't own a piece of the business it runs, or a lousy return on equity.)

You can have it all -- I swear. To prove my point, here are six stocks that shine in all four of those criteria:

Company

Trailing-12-Month
P/E Ratio

Trailing-12-Month
Return on Equity

Insider Ownership

Stryker (NYSE:SYK)

14.7

20%

15%

Garmin (NASDAQ:GRMN)

7.5

27%

44%

GameStop (NYSE:GME)

10.0

18%

4%

Hess (NYSE:HES)

12.6

14%

11%

Fairfax Financial (NYSE:FFH)

5.9

17%

10%

Denbury Resources (NYSE:DNR)

14.3

18%

3%

Source: Capital IQ, a division of Standard & Poor's. Data as of June 12, 2009.
P/E = price-to-earnings ratio.

While these are all great companies, they're also all large and relatively well-known. If you want to combine the same quality-defining attributes I've outlined above with the greatest potential for market-thumping performance, check out what the team at Motley Fool Hidden Gems has to offer. This all-star group of stock pickers is employing the same process that I've used above -- and should have always stuck to in the past -- to find the very best small-cap stocks on Wall Street. You don't have to take my word for it, either. See what they're looking at right now with a free 30-day trial.

And if nothing else, keep my aching portfolio in mind the next time you want to buy a junk stock just because it's cheap.

This article was originally published March 12, 2009. It has been updated.

Fool contributor Matt Koppenheffer owns shares of Berkshire Hathaway and Bank of America, but does not own shares of any of the other companies mentioned. GameStop is a Motley Fool Stock Advisor pick. Berkshire and Stryker are Motley Fool Inside Value picks. Garmin is a Motley Fool Global Gains selection. GameStop is a Stock Advisor selection. The Fool used to own shares of Stryker. The Fool's disclosure policy has never once been caught with its pants down. Of course, it doesn't actually wear pants ...